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Mathematical Hierarchies and Biology
 
Edited by: Boris Mirkin Rutgers University, Piscataway, NJ
F. R. McMorris University of Louisville, Louisville, KY
Fred S. Roberts Rutgers University, New Brunswick, NJ
Andrey Rzhetsky Columbia University, New York City, NY
A co-publication of the AMS and DIMACS
Mathematical Hierarchies and Biology
Hardcover ISBN:  978-0-8218-0762-0
Product Code:  DIMACS/37
List Price: $114.00
MAA Member Price: $102.60
AMS Member Price: $91.20
eBook ISBN:  978-1-4704-3995-8
Product Code:  DIMACS/37.E
List Price: $107.00
MAA Member Price: $96.30
AMS Member Price: $85.60
Hardcover ISBN:  978-0-8218-0762-0
eBook: ISBN:  978-1-4704-3995-8
Product Code:  DIMACS/37.B
List Price: $221.00 $167.50
MAA Member Price: $198.90 $150.75
AMS Member Price: $176.80 $134.00
Mathematical Hierarchies and Biology
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Mathematical Hierarchies and Biology
Edited by: Boris Mirkin Rutgers University, Piscataway, NJ
F. R. McMorris University of Louisville, Louisville, KY
Fred S. Roberts Rutgers University, New Brunswick, NJ
Andrey Rzhetsky Columbia University, New York City, NY
A co-publication of the AMS and DIMACS
Hardcover ISBN:  978-0-8218-0762-0
Product Code:  DIMACS/37
List Price: $114.00
MAA Member Price: $102.60
AMS Member Price: $91.20
eBook ISBN:  978-1-4704-3995-8
Product Code:  DIMACS/37.E
List Price: $107.00
MAA Member Price: $96.30
AMS Member Price: $85.60
Hardcover ISBN:  978-0-8218-0762-0
eBook ISBN:  978-1-4704-3995-8
Product Code:  DIMACS/37.B
List Price: $221.00 $167.50
MAA Member Price: $198.90 $150.75
AMS Member Price: $176.80 $134.00
  • Book Details
     
     
    DIMACS - Series in Discrete Mathematics and Theoretical Computer Science
    Volume: 371997; 388 pp
    MSC: Primary 92; Secondary 05;

    The mathematical approach to the study of hierarchies presents the theoretical basis for many important areas of current scientific investigation. Biology has benefited from this research and has also stimulated the mathematical study of hierarchies.

    This collection presents papers devoted to theoretical, algorithmical, and application issues related to (1) reconstructing hierarchies (trees or ranking) from (dis)similarity or entity-to-character data, (2) using hierarchies for modeling evolution and other processes, and (3) combining (gene) trees.

    The papers in this volume provide a contemporary sample of many new results in hierarchy theory with applications in biology, psychology, data analysis, and systems engineering.

    Features:

    • Mathematical treatment of hierarchies in several interconnected frameworks: set systems, linear subspaces, graph objects, and tree metrics.
    • The relationship of hierarchies to many issues of current application—from learning robots to wavelets to intron evolution to the evolution of language.
    • Solutions to several important problems.

    Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were co-published with the Association for Computer Machinery (ACM).

    Readership

    Graduate students and research mathematicians working in discrete mathematics, computational biology, and data analysis.

  • Table of Contents
     
     
    • Chapters
    • Ancestor-descendant relations and incompatible data: Motivation for research in discrete mathematics
    • Krohn-Rhodes theory, hierarchies & evolution
    • Inferring evolutionary trees from polymorphic characters, and an analysis of the Indo-European family of languages
    • Reconciled trees and incongruent gene and species trees
    • Comparison of annotating duplication, tree mapping, and copying as methods to compare gene trees with species trees
    • Fitting models of intron evolution to aldehyde dehydrogenase data
    • Dissimilarity maps and substitution models: Some new results
    • The performance of the neighbor-joining method of phylogeny reconstruction
    • Concerning the NJ algorithm and its unweighted version, UNJ
    • Order distances in tree reconstruction
    • Circular orders of tree metrics, and their uses for the reconstruction and fitting of phylogenetic trees
    • Estimation of missing distances in path-length matrices: Problems and solutions
    • Complexity issues in hierarchical optimization
    • Nesticity
    • Phylogeny graphs of arbitrary digraphs
    • Agreement metrics for trees revisited
    • Sparse dynamic programming for maximum agreement subtree problem
    • The median function on weak hierarchies
    • Towards a theory of holistic clustering
    • On hierarchies and hierarchical classes models
    • The construction of globally optimal ordered partitions
    • Multiple trees: Fitting two or more tree structures to proximity data
    • Linear embedding of binary hierarchies and its applications
    • Learning algorithms generating multigranular hierarchies
    • Index
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 371997; 388 pp
MSC: Primary 92; Secondary 05;

The mathematical approach to the study of hierarchies presents the theoretical basis for many important areas of current scientific investigation. Biology has benefited from this research and has also stimulated the mathematical study of hierarchies.

This collection presents papers devoted to theoretical, algorithmical, and application issues related to (1) reconstructing hierarchies (trees or ranking) from (dis)similarity or entity-to-character data, (2) using hierarchies for modeling evolution and other processes, and (3) combining (gene) trees.

The papers in this volume provide a contemporary sample of many new results in hierarchy theory with applications in biology, psychology, data analysis, and systems engineering.

Features:

  • Mathematical treatment of hierarchies in several interconnected frameworks: set systems, linear subspaces, graph objects, and tree metrics.
  • The relationship of hierarchies to many issues of current application—from learning robots to wavelets to intron evolution to the evolution of language.
  • Solutions to several important problems.

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1–7 were co-published with the Association for Computer Machinery (ACM).

Readership

Graduate students and research mathematicians working in discrete mathematics, computational biology, and data analysis.

  • Chapters
  • Ancestor-descendant relations and incompatible data: Motivation for research in discrete mathematics
  • Krohn-Rhodes theory, hierarchies & evolution
  • Inferring evolutionary trees from polymorphic characters, and an analysis of the Indo-European family of languages
  • Reconciled trees and incongruent gene and species trees
  • Comparison of annotating duplication, tree mapping, and copying as methods to compare gene trees with species trees
  • Fitting models of intron evolution to aldehyde dehydrogenase data
  • Dissimilarity maps and substitution models: Some new results
  • The performance of the neighbor-joining method of phylogeny reconstruction
  • Concerning the NJ algorithm and its unweighted version, UNJ
  • Order distances in tree reconstruction
  • Circular orders of tree metrics, and their uses for the reconstruction and fitting of phylogenetic trees
  • Estimation of missing distances in path-length matrices: Problems and solutions
  • Complexity issues in hierarchical optimization
  • Nesticity
  • Phylogeny graphs of arbitrary digraphs
  • Agreement metrics for trees revisited
  • Sparse dynamic programming for maximum agreement subtree problem
  • The median function on weak hierarchies
  • Towards a theory of holistic clustering
  • On hierarchies and hierarchical classes models
  • The construction of globally optimal ordered partitions
  • Multiple trees: Fitting two or more tree structures to proximity data
  • Linear embedding of binary hierarchies and its applications
  • Learning algorithms generating multigranular hierarchies
  • Index
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.